The following discussion of the background art is intended to facilitate an understanding of the present invention only. It should be appreciated that the discussion is not an acknowledgement or admission that any of the material referred to is or was part of the common general knowledge as at the priority date of the application.
For the purposes of pulsed NQR, any solid sample containing quadrupole nuclei can be characterised by three parameters: the spin-lattice relaxation time T1, the spin-spin relaxation time T2 and the time of the induction signal damping T2*.
From the point of view of practical use in NQR, and on the basis of the above parameters, multi-pulse sequences can be classified into the following general groups:
Group I:
Sequences of single pulses, which can include multi-pulse sequences of any type, if intervals between the pulses in these sequences exceed the spin-lattice relaxation time T1.
Group II:
Sequences with intervals between pulses τ that are within the limits T2*<τ<<T1.
All echo-sequences (sequences composed of a certain number of pulses which are organised in such a way that the NQR signal is formed not directly after the radio frequency irradiation pulse, but after a certain delay, necessary for refocussing the magnetic momentum of the sample nuclei) could also be regarded as belonging to this type of sequence, because in the optimal formation of the echo signal the condition T2*<τ<T2 generally holds true.
One of the main peculiarities of this type of sequence is its apability to saturate the quadrupolar spin system of the sample. This can be observed when a multi-pulse sequence of this type is used, as the chain of NQR signals measured in the observation windows between the pulses decays with a time constant T1e, which is called the effective relaxation time and lies within the limits of T2≦T1e<T1 (or, to be more precise, within the limits of T2≦T1e<T1ρ, where T1ρ is the relaxation time in rotating frame, with the permanent condition of T1ρ<T1).
Group III:
    Stochastic Sequences.Group IV:
Multi-pulse sequences of the Steady State Free Precession (SSFP) type. Intervals between pulses in these sequences (τ) fulfil the condition of τ<T2*.
This type can include quite complex formations, containing not only SSFP sequences but also special techniques for destroying the SSFP state; this “destruction” can be achieved by including the magnetic field gradient pulses, by using composite pulses so as to form a special phase alternation of the RF carrier frequency, etc. The purpose of this “destruction” is to overcome one of the main drawbacks of SSFP sequences—intensity anomalies, which manifest themselves by the decreasing amplitude and the increasing rate of signal decay when the parameters of an irradiating sequence approach resonance conditions
            n      ·              ω        eff              =          m      ·              π        τ              ,where τ is the interval between pulses of the sequence, n and m are whole numbers, an effective field ωeff substitutes the effect of the RF pulses and the resonance offsetGroup V:
Complex types of multi-pulse sequences containing sub-sequences of two or more of the above types of multi-pulse sequences.
The fifth group does not have any individual physical characteristics that do not relate to at least one of the previous groups. Therefore, only aspects of the first four groups of sequences in the above classification will be considered further.
Group I
Advantages:
    1. No intensity anomalies;    2. No saturation problem, and therefore no signal decay.Disadvantages:    1. At long T1 times the detection time of a sample can exceed any practically acceptable limits;    2. Single pulses can only create a free induction decay (FID) signal, entirely determined—as well as magneto-acoustic ringing, piezo-electric effects and the spurious signals of the resonance circuit of the NQR detector probe—by the pulse that generated it. The consequence of this is that the NQR signal measured when the standard means of damping spurious signals is used, is considerably weakened, and often disappears completely.
Because of these disadvantages the first group of sequences is of little benefit for practical use in NQR.
Group II
Advantages:
    1. Possibility of generating echo-signals with parameters depending not only on the last pulse but also on the preceding pulses of the sequence which can be used to cancel spurious signals while keeping and sometimes even increasing the intensity of the NQR signal;    2. Possibility of generating echo-signals at times exceeding “dead time” of the receive system of the spectrometer;    3. Possibility of saturating the sample, which enables the measurement of the spurious signals together with the NQR signals, then spurious signals only, after which the latter can be subtracted.Disadvantages:    1. Time available for accumulating the NQR signal is limited by the time constant T1e<T1;    2. Echo sequences (which is one of the main advantages of this group), are not particularly effective in detecting a number of substances that have a little or zero asymmetry parameter, as the amplitude of echo-signals decreases with the decrease of the asymmetry parameter.Group IIIAdvantages:    1. No intensity anomalies;    2. Possibility of saturating the sample to enable subtraction of spurious signals. Saturation in this case is entirely determined by the flip angle of the pulses and the time of spin-lattice relaxation T1;    3. The stochastic resonance requires lower peak power. The peak power can be tens and even hundreds of times lower than when using coherent pulses and still achieve similar sensitivity.Disadvantages:    1. Stochastic sequences belong to saturating sequences; however the saturation of the spin system limits the time of the NQR signal accumulation, as is the case with Group II sequences, which is equivalent to a loss of sensitivity; stochastic sequences do not produce the same advantages that Group II sequences can offer using echo signals.    2. Using a stochastic sequence for saturating a sample does not give any advantages as compared with normal saturation methods that use coherent pulses, but is technically more complicated to realise.    3. Using stochastic sequences requires introducing a random delay in the timing of the radio frequency pulses, but there are cases where the timing between radio frequency pulses is relatively short and any delays introduced in the timing tend to greatly increase the spectrometer time required to obtain the desired time average spectral data.
The general conclusion about the use of stochastic sequences in NQR for identification of explosive and narcotic substances is that they are more technically complicated to produce and the achieved sensitivity as a rule does not exceed that of coherent sequences.
Group IV
Advantages:
    1. it is possible to receive a continuous chain of signals if the requirement
      n    ·          ω      eff        ≠      m    ·          π      τ      is met, which ensures unlimited time for signal accumulation. Here, τ is the pulse spacing of the sequence, n and m are whole numbers, and ωeff represents the effective field which substitutes the effect of the RF pulses and the resonance offset.    2. it is possible to receive an NQR signal phase that is different from the phase of irradiating pulses, which can be used for cancelling intensity anomalies, or for subtracting spurious signals;    3. Comparatively little RF power is required for detecting samples in large volumes.Disadvantages:    1. Intensity anomalies;    2. Higher requirements due to the time of damping ringing and the time of equipment insensitivity at short T2*.
When the requirement
      n    ·          ω      eff        ≠      m    ·          π      τ      is met, the SSFP sequences allow achievement of a greater signal-to-noise ratio per unit of time than any other multi-pulse sequences used for exciting the quadrupole spin system.
However, complying with this requirement cannot be guaranteed in practice because the exact value of the resonance offset in most cases is unknown due to the fact that the exact temperature of the sample is not known either.
Thus the dependence of the signal intensity on the resonance offset when using the SSFP sequences is characterised by the existence of intensity anomalies and these intensity anomalies make the SSFP group sensitive to the changes in the resonance frequency of the quadrupole spin system during temperature changes.
In the solid state when irradiating sequence parameters approach the resonance conditions, intensity anomalies are manifested specifically by the reduction of the amplitude and increase in damping of the signal as indicated by the equation:
            n      ·              ω        eff              =          m      ·                        π          τ                .              ,
If the temperature of a sample leads to the setting of frequency ωQ of the quadrupole transition in the sample such that the resonance condition
      n    ·          ω      eff        =      m    ·          π      τ      is met, then the chain of the NQR signals decays with time constant T1e, which is the function of the frequency offset, pulse interval and the flip angle. At short T1 times (T1e<T1) the decay happens quickly, decreasing sharply the sensitivity of detection, which can result in a sharp decline in the signal intensity or even in the complete loss of information about the presence (or absence) of the sample in the examined volume.
For a number of substances, the temperature dependence of the resonance frequencies of quadrupolar nuclei is quite considerable. For example, for RDX at frequency ν+=5.192 MHz at temperatures close to room temperature, the change in 14N resonance frequency is −520 Hz/° K, for PETN at the 14N frequency ν+=890 kHz it is −160 Hz/° K, for KNO3 at nitrogen-14 line ν+=567 kHz it is −140 Hz/° K etc.
The maximum sensitivity in most cases is achieved in practice when using SSFP sequences, whereby if the parameters are properly chosen, the biggest signal to noise ratio in unit time may be acheived.
The first SSFP sequence consisting of identical coherent RF pulses was used in research relating to Nuclear Magnetic Resonance (NMR) in 1951 and was later studied in great detail. Subsequently in 1965, this sequence was first used in NQR research for measuring the T1 of the 14N resonance line in hexamethylene tetramine. Then a two-frequency version of this sequence was used to measure relaxation times in urea, which involved the simultaneous irradiation of the two 14N resonance transitions ν+ and ν− with two SSFP sequences.
Later, a sequence with identical coherent RF pulses and a nonzero resonance offset was used. Back then, some combinations of SSFP sequences were used to solve the problem of intensity anomalies in detecting explosives by the NQR method.
The following method of suppressing intensity anomalies was suggested.
To irradiate the sample, the basic version of the SSFP sequences was used—a sequence of coherent equally spaced pulses with a flip angle φ and the repetition cycle τ: [τ/2−φ−τ/2]n, where n is the number of the sequence cycles (it is also possible to write it down as [φ−τ]n).
The irradiation was done with different series of pulses, with the carrier frequency of pulses in each series corresponding to one of the two values: f0 and
            f      0        ±          2      τ        ,where f0 is the frequency close to the resonance frequency.
If there was no signal when irradiating with the series that had the carrier frequency f0, the sample would then be irradiated with the other series with the carrier frequency
      f    0    ±            2      τ        .  
The difference in the frequency of both carrier frequencies corresponds to the difference between the frequencies at which the maximum and the minimum signal intensity was observed.
It was then suggested to use combinations of sequences with phase alternating (PAPS) and without phase alternating (NPAPS): [φx−τ−φx−τ]n[φx−τ−φ−x−τ]n, where the bottom index at the flip angle sign φ designates the phase of the carrier frequency for the RF pulse, and n is the number of cycles of the sequence.
In this case, if in the intervals corresponding to PAPS, the maximum signal was achieved, then in the intervals corresponding to NPAPS, the minimum signal would be observed. Such sequence combinations permitted irradiating the sample without switching the carrier frequency.
Essentially, two separate methods were proposed by which to perform the signal accumulation.
In the first method, the signals received after φ−x pulses of the PAPS sequence were subtracted from the signals received after φx pulses of the NPAPS sequence, and those received after φx of the PAPS sequence were added together with the resultant signal. This allowed not only a decrease in intensity anomalies, but also elimination of magneto-acoustic ringing.
In the second method, the signals received after φx pulses of both PAPS and NPAPS sequences are added together, and the signals received after φ−x pulses are subtracted from the resultant signal.
The maximum accumulated signal achieved by using either method of accumulation is less than the maximum achieved when using only NPAPS or PAPS by √{square root over (2)} times.
For the sake of comparison, as shown in FIG. 1, the curves corresponding to two dependencies of NQR signal on the frequency received for NaNO2 are shown, after irradiation with NPAPS and PAPS sequences using the accumulation rules determined by the first method described above (curve 1) and the second method (curve 2), respectively.
Thus all methods described above for eliminating temperature effects associated with intensity anomalies at a prescribed number of accumulations result in decreasing the intensity of the measured signal, as compared with the maximum signal intensity possible to measure arising from using only one of the SSFP sequences.